Negative numbers
Negative numbers are
numbers that are less than zero.
When you first encounter negative numbers they can be perplexing.
How can a bowl contain less than zero oranges?
In fact, the
counting numbers cannot be negative for this reason. It makes no sense.
But when we use
scalar numbers,
we are measuring something like temperature or height, negative values are useful.
(See Uses of negative numbers.)
We take a fixed point and call that zero. Measurements one way are positive, and they are negative the other way. Zero is neither positive nor negative.
Try this
Adjust the arrow to see how negative numbers lie to the left of zero on the number line. The applet
will not allow you to set the arrow to zero or a positive number.
The '–' sign
Negative numbers are indicated by placing a dash ( – ) sign in front, such as –5, –12.77.
A negative number such as –6 is spoken as 'negative six'.
It also means 'subtract'
An unfortunate thing in math is that the ' – ' symbol is used for two different things.
It signifies a negative number, as described above, but it also means 'subtract' or 'minus'. For example
5–3 means 'subtract 3 from 5' with a result of 2. Here, the minussign means subtraction.
So, when talking about a negative number such as –4, train yourself to say 'negative four' to avoid the confusion.
The same confusion happens with the plus ( + ) sign. See
Positive numbers.
See also Doing arithmetic with positive and negative numbers.
Comparing numbers
With all numbers, whether they are negative, zero or positive:
 A number is greater than another when it is to the right on the number line.
 Conversely a number is less than another when it is to the left on the number line.
So for example
 –4 is less than –1
 zero is greater than –120
 90 is greater than –1
Larger /smaller  watch out!
Avoid the words 'larger', 'bigger' and 'smaller' when comparing numbers. They can fool you.
For example is 1000 larger than 4?
It may look like it, but is not. 1000 is less than 4 because it is to the left on the number line. But when you use the word 'larger'
you may think otherwise. Avoid these two words in math. Use 'less than' and 'greater than' instead.
An overview of the types of numbers that are used in math. Links to other pages explaining each type in depth. Explains also that some numbers are not numbers at all.
Numbers can be positive, negative or zero. Positive numbers are the ones you most encounter in everyday life, such as 34, 9.22, etc. When shown on a number line, they are the ones usually drawn on the right of zero, getting larger as you move to the right.
An animated elevator in a skyscraper is used to illustrate how the height of the elevator can be negative in the basement.
While you are here..
... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone.
However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site?
When we reach the goal I will remove all advertising from the site.
It only takes a minute and any amount would be greatly appreciated.
Thank you for considering it! – John Page
Become a patron of the site at patreon.com/mathopenref
Other number topics
Scalar numbers
Counting numbers
Numbers that have factors
Special values
(C) 2011 Copyright Math Open Reference. All rights reserved
